(5r-3)(r-1)=0

Solution for (5r-3)(r-1)=0 equation:

Simplifying
(5r + -3)(r + -1) = 0

Reorder the terms:
(-3 + 5r)(r + -1) = 0

Reorder the terms:
(-3 + 5r)(-1 + r) = 0

Multiply (-3 + 5r) * (-1 + r)
(-3(-1 + r) + 5r * (-1 + r)) = 0
((-1 * -3 + r * -3) + 5r * (-1 + r)) = 0
((3 + -3r) + 5r * (-1 + r)) = 0
(3 + -3r + (-1 * 5r + r * 5r)) = 0
(3 + -3r + (-5r + 5r2)) = 0

Combine like terms: -3r + -5r = -8r
(3 + -8r + 5r2) = 0

Solving
3 + -8r + 5r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -5r)(1 + -1r) = 0

Subproblem 1
Set the factor '(3 + -5r)' equal to zero and attempt to solve:

Simplifying
3 + -5r = 0

Solving
3 + -5r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5r = 0 + -3
-5r = 0 + -3

Combine like terms: 0 + -3 = -3
-5r = -3

Divide each side by '-5'.
r = 0.6

Simplifying
r = 0.6
Subproblem 2
Set the factor '(1 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1r = 0 + -1
-1r = 0 + -1

Combine like terms: 0 + -1 = -1
-1r = -1

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {0.6, 1}